Details

Time bar (total: 13.2s)

sample33.0ms

Algorithm
intervals
Results
19.0ms269×body80valid

simplify77.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
01115
12114
24014
35614
47614
58814
69214
done9214

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.8b

localize11.0ms

Local error

Found 2 expressions with local error:

0.7b
(- (* b c) (* a d))
24.4b
(/ (- (* b c) (* a d)) (fma c c (* d d)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/r* associate-/l*
2×pow1 expm1-log1p-u flip3-- flip-- log1p-expm1-u associate-/l/
1×cbrt-undiv sub-neg frac-2neg fma-neg diff-log div-sub div-exp prod-diff clear-num div-inv
Counts
2 → 48
Calls
2 calls:
10.0ms
(- (* b c) (* a d))
21.0ms
(/ (- (* b c) (* a d)) (fma c c (* d d)))

series191.0ms

Counts
2 → 6
Calls
2 calls:
62.0ms
(- (* b c) (* a d))
128.0ms
(/ (- (* b c) (* a d)) (fma c c (* d d)))

simplify2.5s

Counts
54 → 54
Iterations

Useful iterations: done (2.5s)

IterNodesCost
087931
1214906
2710807
32547807
done5000801

prune248.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 16.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot c d)
0.2b
(* (/ 1 (hypot c d)) (/ (- (* b c) (* a d)) (hypot c d)))
0.7b
(- (* b c) (* a d))
16.1b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
34×times-frac
28×add-exp-log *-un-lft-identity
26×add-cube-cbrt
18×add-cbrt-cube
13×associate-*r* associate-*l*
9×div-exp
8×prod-exp
6×pow1 add-log-exp unswap-sqr
5×cbrt-undiv
4×expm1-log1p-u cbrt-unprod log1p-expm1-u
3×associate-/r* div-inv associate-/l*
2×rec-exp flip3-- 1-exp flip-- associate-/l/
1×frac-times sub-neg hypot-udef frac-2neg fma-neg diff-log div-sub associate-*r/ prod-diff pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 116
Calls
4 calls:
0.0ms
(hypot c d)
49.0ms
(* (/ 1 (hypot c d)) (/ (- (* b c) (* a d)) (hypot c d)))
22.0ms
(- (* b c) (* a d))
26.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series489.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(hypot c d)
230.0ms
(* (/ 1 (hypot c d)) (/ (- (* b c) (* a d)) (hypot c d)))
47.0ms
(- (* b c) (* a d))
137.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify1.7s

Counts
128 → 128
Iterations

Useful iterations: 2 (256.0ms)

IterNodesCost
01702225
14542076
215271817
done50001817

prune828.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot c d)
0.1b
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
0.7b
(- (* b c) (* a d))
16.1b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
54×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×associate-/l*
11×add-exp-log add-cbrt-cube
6×associate-/r* div-inv add-log-exp
4×pow1 cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×div-sub associate-/l/
2×flip3-- frac-2neg clear-num flip--
1×sub-neg hypot-udef fma-neg diff-log prod-diff
Counts
4 → 131
Calls
4 calls:
0.0ms
(hypot c d)
25.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
11.0ms
(- (* b c) (* a d))
25.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series446.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(hypot c d)
165.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
61.0ms
(- (* b c) (* a d))
168.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify2.4s

Counts
143 → 143
Iterations

Useful iterations: done (2.4s)

IterNodesCost
01932874
14522796
212512600
344892545
done50002540

prune448.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot c d)
0.1b
(/ (- (/ c (/ (hypot c d) b)) (* d (/ a (hypot c d)))) (hypot c d))
6.8b
(* d (/ a (hypot c d)))
10.7b
(/ c (/ (hypot c d) b))

rewrite148.0ms

Algorithm
rewrite-expression-head
Rules
94×times-frac
67×add-sqr-sqrt
62×add-cube-cbrt *-un-lft-identity
16×add-exp-log associate-/r* add-cbrt-cube
13×associate-*r*
7×div-inv
6×pow1 associate-/l*
5×cbrt-undiv div-exp
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*l* associate-/l/
2×frac-2neg associate-*r/ prod-exp clear-num cbrt-unprod unswap-sqr
1×hypot-udef flip3-- div-sub pow-prod-down associate-/r/ *-commutative frac-sub flip--
Counts
4 → 149
Calls
4 calls:
0.0ms
(hypot c d)
110.0ms
(/ (- (/ c (/ (hypot c d) b)) (* d (/ a (hypot c d)))) (hypot c d))
20.0ms
(* d (/ a (hypot c d)))
9.0ms
(/ c (/ (hypot c d) b))

series727.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(hypot c d)
446.0ms
(/ (- (/ c (/ (hypot c d) b)) (* d (/ a (hypot c d)))) (hypot c d))
95.0ms
(* d (/ a (hypot c d)))
116.0ms
(/ c (/ (hypot c d) b))

simplify1.1s

Counts
161 → 161
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02672504
15902400
218202216
done50002214

prune508.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

regimes108.0ms

Accuracy

0% (0.8b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 0.8b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
01423
11919
done1919

end0.0ms

sample855.0ms

Algorithm
intervals
Results
522.0ms8494×body80valid